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Journal of Experimental and Theoretical Physics

Multiply connected Fermi sphere and fermion condensation

MIKHAIL V. ZVEREV, M. Baldo

Published Dec 1, 1998• 32 citations
Publisher

Abstract

We examine the structure of the ground state of a homogeneous Fermi liquid beyond the instability point of the Fermi-like quasiparticle momentum distribution in the effective-functional method with a strong repulsive effective interaction. A numerical study of the initial stage of rearrangement of the ground state, based on a simple effective functional, showed that there exists a temperature T 0 , above which the behavior of the system is the same as in the theory of fermion condensation, and for T < T 0 the scenario of rearrangement of the ground state is different. At low temperatures an intermediate structure arises, with a multiply connected quasiparticle momentum distribution. The transition of this structure with growth of the coupling constant to a state with a fermion condensate is discussed.

DOI
10.1134/1.558604

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We examine the structure of the ground state of a homogeneous Fermi liquid beyond the instability point of the Fermi-like quasiparticle momentum distribution in the effective-functional method with a strong repulsive effective interaction. A numerical study of the initial stage of rearrangement of the ground state, based on a simple effective functional, showed that there exists a temperature T 0 , above which the behavior of the system is the same as in the theory of fermion condensation, and for T < T 0 the scenario of rearrangement of the ground state is different. At low temperatures an intermediate structure arises, with a multiply connected quasiparticle momentum distribution. The transition of this structure with growth of the coupling constant to a state with a fermion condensate is discussed.
The structure of the ground state beyond the instability point of the quasiparticle system with a Fermi-step momentum distribution is studied within the model of a Fermi liquid with a strong repulsive interaction. A ground-state rearrangement occurs as the interaction strength is increased beyond a certain critical value. Numerical investigation of the initial stage of this structural transition shows that there are two temperature regions, corresponding to different scenarios of the rearrangement. While for temperature T larger than some characteristic temperature the behaviour of the system is the same as that in the case of fermion condensation, for an intermediate structure with a multi-connected quasiparticle momentum distribution arises.
We consider a system of fermions with mass m and model repulsive interaction U(q) = g/\sqrt{q^2 + q_0^2}, where q is the momentum transfer, q_0 the screening constant, and g > 0 the coupling constant. It is shown that at g > g_cr > 3π^2/m the system ground state is changed from fully occupied Fermi sphere to multiconnected Fermi sphere (MFS), consisting in N fully occupied spherical layers (icebergs) separated by empty spacers. An effective description is developed for such states at N >> 1, showing their tendency at N \to \infty to the Fermi condensate (FC) state known for the model U(q) = g/q [Khodel, Shaginyan, JETP Lett., 51, 553, 1990]. At finite temperatures, a crossover is predicted from the Fermi liquid behavior of MFS with effective mass m^* \sim m N/ln(N) to non-Fermi-liquid behavior with m^* \propto 1/T at T > T^* \sim T_F ln(N)/N.
Opportunities for topological phase transitions in strongly correlated Fermi systems near a quantum critical point are explored as an alternative to collective scenarios for experimentally observed departures from standard Fermi-liquid behavior. Attention is focused on a quantum critical point at which the effective mass is divergent due to vanishing of the quasiparticle group velocity at the Fermi surface. Working within the original Landau quasiparticle theory, it is demonstrated that the quasiparticle picture can remain meaningful beyond the quantum critical point through rearrangements of the unstable normal Fermi surface and quasiparticle spectrum. Two possibilities emerge at zero temperature, depending on whether the quasiparticle interaction is regular or singular at zero momentum transfer. In the regular case, one type of topological phase transformation leads to a state with a multiconnected Fermi surface. In the singular case, another type of topological phase transition leads to an exceptional state containing a fermion condensate – the Fermi surface swells into a volume in momentum space, within which partial occupation prevails and quasiparticle energies are pinned to the chemical potential. As the temperature increases from zero to a characteristic value Tm, a crossover can occur from the state with multiple Fermi surfaces to that containing a fermion condensate.
The appearance of the fermion condensation, which can be compared to the Bose-Einstein condensation, in different Fermi liquids is considered; its properties are discussed; and a large amount of experimental evidence in favor of the existence of the fermion condensate (FC) is presented. We show that the appearance of FC is a signature of the fermion condensation quantum phase transition (FCQPT), which separates the regions of normal and strongly correlated liquids. Beyond the FCQPT point, the quasiparticle system is divided into two subsystems, one containing normal quasiparticles and the other, FC, localized at the Fermi level. In the superconducting state, the quasiparticle dispersion in systems with FC can be represented by two straight lines, characterized by effective masses M FC * and M L * and intersecting near the binding energy E 0, which is of the order of the superconducting gap. The same quasiparticle picture and the energy scale E 0 persist in the normal state. We demonstrate that fermion systems with FC have features of a “quantum protectorate” and show that strongly correlated systems with FC, which exhibit large deviations from the Landau Fermi liquid behavior, can be driven into the Landau Fermi liquid by applying a small magnetic field B at low temperatures. Thus, the essence of strongly correlated electron liquids can be controlled by weak magnetic fields. A reentrance into the strongly correlated regime is observed if the magnetic field B decreases to zero, while the effective mass M* diverges as $$M^ * \propto {1 \mathord{\left/ {\vphantom {1 {\sqrt B }}} \right. \kern-\nulldelimiterspace} {\sqrt B }}$$ . The regime is restored at some temperature T∗∝BT^ * \propto \sqrt B T∗∝B​ . The behavior of Fermi systems that approach FCQPT from the disordered phase is considered. This behavior can be viewed as a highly correlated one, because the effective mass is large and strongly depends on the density. We expect that FCQPT takes place in trapped Fermi gases and in low-density neutron matter, leading to stabilization of the matter by lowering its ground-state energy. When the system recedes from FCQPT, the effective mass becomes density independent and the system is suited perfectly to be conventional Landau Fermi liquid.
The rearrangement of the Fermi surface in a diluted two-dimensional electron gas beyond the topological quantum critical point has been examined within an approach based on the Landau theory of Fermi liquid and a nonperturbative functional method. The possibility of a transition of the first order in the coupling constant at zero temperature between the states with a three-sheet Fermi surface and a transition of the first order in temperature between these states at a fixed coupling constant has been shown. It has also been shown that a topological crossover, which is associated with the joining of two sheets of the Fermi surface and is characterized by the maxima of the density of states N(T) and ratio C(T)/T of the specific heat to the temperature, occurs at a very low temperature T ⋄ determined by the structure of a state with the three-sheet Fermi surface. A momentum region where the distribution n(p, T) depends slightly on the temperature, which is manifested in the maximum of the specific heat C(T) near T *, appears through a crossover at temperatures T ∼ T * > T ⋄. It has been shown that the flattening of the single-particle spectrum of the strongly correlated two-dimensional electron gas results in the crossover from the Fermi liquid behavior to a non-Fermi liquid one with the density of states N(T) ∝ T −α with the exponent α }~ 2/3.
The rearrangement of single-particle degrees of freedom of a dilute two-dimensional electron gas in the vicinity of the quantum critical point is examined within a microscopic approach. It is shown that just beyond the critical point, the Landau state undergoes self-consistent rearrangement of the quasiparticle spectrum and momentum distribution. At very low temperatures, there emerges a multi-connected quasiparticle momentum distribution. With increasing temperature, two crossovers occur: a fermion condensate appears in the first and disappears in the second, giving way to universal non-Fermi-liquid behavior. Manifestations of these crossovers in thermodynamic properties of the electron gas are studied and characterized. The four quasiparticle phases predicted to exist in the vicinity of the critical point are collected in a schematic phase diagram.